A reliable potential in the standard inflationary paradigm requires proposing a mechanism to remove the flatness problem as one of the main shortcomings of the hot big bang theory. Natural inflation (NI) overcomes this problem using a Pseudo-Nambu-Goldstone boson as inflaton with a flat potential [1]}, [2]}
\(V(\varphi )=V_{0}\Big (1+\cos (\frac{\varphi }{f})\Big ),\) 
